Question

A parabolic archway is 12 meters high at the vertex. at a height of 10 meters, the width of the archway is 8 meters. how wide is the archway at ground level?

Answer 1

To solve this problem you must apply the proccedure shown below:

1. You have that the parabola is 12 meters high at the vertex and at a height of 10 meters, the width is 8 meter.

2. Therefore, you have:

x^2=-4a(y^2-k)
4^2=-4a(10-12)
16=-40a+48
16=8a
a=16/8
a=2

y=0
x^2=-8(0-12)
x^2=96
x=√96
x=9.79x2
x=19.58

3. Therefore, as you can see, the answer is: 19.58 meters.